Transitions in coherent oscillations between two trapped Bose-Einstein condensates

By solving numerically the tunneling quantum dynamics between two trapped B ose-Einstein condensates (BEC's), we find two distinct time scales. On the short time scale, we recover semiclassical predictions such as "macroscopic quantum self-trapping'' and the "amplitude transition," first studied in t he polaron context, and the "pi states," previously discovered in the conte xt of BEC's. On a much longer time scale, quantum dynamics shows that self- trapping is destroyed in contrast to semiclassical behavior. However, this time scale increases exponentially with the total number of condensate atom s, indicating that self-trapping and "pi states'' would be relevant and exp erimentally observable in the tunneling of BEC's. [S1050-2947(99)51409-1].